No, your wrong.
For a solution, ppm just means mg of solute per litre of solution. You get 1 mg of salt and dissolve it in a litre of water you have a 1 ppm NaCl solution.
For a solid, it means mg of solute per kg of solid. It is perfectly reasonable to use ppm to describe the concentration of a solute in a solid, for example look at every Uranium drill hole and resource definition.
Ppm can also describe a concentration of any solute in a gas. eg an aerosol.
It can be used for anything.
For some reason I did a PhD in chemistry, so I unfortunately know this stuff.
Dealing with numbers of atoms and Avagadro's number is ridiculous. Start working with numbers with 23 zero's after the number and you soon learn how meaningless of an activity it is.
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